Advertisements
Advertisements
प्रश्न
If `x^4 + 1/x^4 = 194, "find" x^3 + 1/x^3`
Advertisements
उत्तर
In the given problem, we have to find the value of `x^3 + 1/x^3.`
Given: `x^4 + 1/x^4 = 194`
We know that,
`(x^2 + 1/x^2)^2 = x^4 + 1/x^4 + 2` ...[Using (a + b)2 = a2 + b2 + 2ab]
Now, substituting the given value
`(x^2 + 1/x^2)^2 = 194 + 2`
∴ `(x^2 + 1/x^2)^2 = 196`
∴ `x^2 + 1/x^2 = sqrt196`
∴ `x^2 + 1/x^2 = +-14`
Let’s relate it to `x^3 + 1/x^3`
`(x + 1/x)^2 = x^2 + 1/x^2 + 2` ...[Using (a + b)2 = a2 + b2 + 2ab]
`(x + 1/x)^2 = 14 + 2`
∴ `x + 1/x = sqrt16`
∴ `x + 1/x = +-sqrt4`
Thus,
`x^3 + 1/x^3 = (x + 1/x)^3 - 3(x + 1/x)`
`x^3 + 1/x^3 = (4)^3 - 3(4)`
`x^3 + 1/x^3 = 64 - 12`
∴ `x^3 + 1/x^3 = +-52`
संबंधित प्रश्न
Expand the following, using suitable identity:
(–2x + 3y + 2z)2
Write the following cube in expanded form:
`[3/2x+1]^3`
Factorise the following:
`27p^3-1/216-9/2p^2+1/4p`
Verify that `x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]`
Evaluate following using identities:
(a - 0.1) (a + 0.1)
Evaluate the following using identities:
(399)2
Simplify the following: 175 x 175 x 2 x 175 x 25 x 25 x 25
Simplify: `(a + b + c)^2 - (a - b + c)^2`
If a + b = 10 and ab = 21, find the value of a3 + b3
If \[x^2 + \frac{1}{x^2} = 98\] ,find the value of \[x^3 + \frac{1}{x^3}\]
Find the following product:
(4x − 5y) (16x2 + 20xy + 25y2)
Find the following product:
\[\left( \frac{x}{2} + 2y \right) \left( \frac{x^2}{4} - xy + 4 y^2 \right)\]
Find the following product:
Mark the correct alternative in each of the following:
If \[x + \frac{1}{x} = 5\] then \[x^2 + \frac{1}{x^2} = \]
(x − y) (x + y) (x2 + y2) (x4 + y4) is equal to ______.
The product (x2−1) (x4 + x2 + 1) is equal to
Find the square of : 3a - 4b
If a + b = 7 and ab = 10; find a - b.
Use the direct method to evaluate :
(x+1) (x−1)
Use the direct method to evaluate :
(xy+4) (xy−4)
Simplify by using formula :
(x + y - 3) (x + y + 3)
Evaluate the following without multiplying:
(999)2
Evaluate, using (a + b)(a - b)= a2 - b2.
999 x 1001
If `"a" - 1/"a" = 10`; find `"a"^2 - 1/"a"^2`
If p + q = 8 and p - q = 4, find:
pq
If x + y = 1 and xy = -12; find:
x2 - y2.
If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :
`"a"^2 + (1)/"a"^2`
If x + y + z = p and xy + yz + zx = q; find x2 + y2 + z2.
If `"r" - (1)/"r" = 4`; find : `"r"^4 + (1)/"r"^4`
Give possible expressions for the length and breadth of the rectangle whose area is given by 4a2 + 4a – 3.
